What is the integral of (sin(x^2))/x ?

The integral of (sin(x^2))/x is 1/2 \Si(x^2)+C

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integral of (sin(x^2))/x

integral

\frac{sin ( x ^{2} )}{x}

\frac{1}{2} Si (x^{2}) + C

Solution steps

\int \frac{sin ( x ^{2} )}{x} d x

Apply u-substitution

: \int \frac{sin ( u )}{2 u} d u

= \int \frac{sin ( u )}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{sin ( u )}{u} d u

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= \frac{1}{2} Si (u)

Substitute back

u = x^{2}

= \frac{1}{2} Si (x^{2})

Add a constant to the solution

= \frac{1}{2} Si (x^{2}) + C

\frac{1}{x} \cdot cos^{2} (x)

1 + e^{- x} sin (4 x)

2 x^{- 3}

(4 - x^{2})^{1.5}

(1 - x^{2})^{3}

What is the integral of (sin(x^2))/x ?
The integral of (sin(x^2))/x is 1/2 \Si(x^2)+C